Psicorps in X-Com: UFO Defense. Hard as hell to acquire, as you need to capture a psi-using alien that is blasting you with said psi-abilities (often straight at the easily affected guy that it can't even see), interrogate the alien, research the tech, build the required buildings, then wait until the month ends for results from said building. If you're extremely lucky, you'll have this by the 4th month, else you might have to wait until the lategame aliens show up. But it was well worth it. First off, you get to see the Psi-Defense stat of your units, eventually allowing you to get a team entirely immune to psi-attacks. The abilities themselves are powerful as well. The more accurate skill causes the target to panic, making them an easy kill. The other skill is Mind Control, a skill so powerful that you can use it to win the final mission on the first turn singlehandedly. Apocalypse nerfed it from Game Breaker to merely stupidly powerful (the second was merely so hard you actually needed it to win on the higher levels). You can use it to mind-control a zombie, kill it, then you have a pet Chrysalid.
And then there's the Blaster Launcher, a weapon that could send a missile out the door of your transport, over the heads of your units, down through the door of the UFO and up the elevator shaft to blow a hole in the otherwise impregnable UFO hull material. Or alternately just take out a Sectopod in one shot. It's successor, the DPT Launcher, was nerfed in a way you can only fire it underwater... unless you consider that you troops can still reaction-fire it! Not to mention that one of the resources necessary to make ammo for it is more abundant in the sequel.
Avenger/Leviathan craft. Though the basic interception unit is so weak that * every* alien craft can outrun it, these two can outrun and outgun even the strongest alien craft - with a bit of a twist: if they survive, they become TOTALLY USELESS for about a month until repairs are done (plus they consume valuable resources to even keep flying). Meanwhile, aliens are happily wreaking havoc...
You can actually stick any craft weapon on any ship capable of dogfighting. Cue the Plasma Cannon: not overly powerful or fast, but it's range exceeds that of any UFO except the largest Battleships, it's ammo is free, and it has plenty of the stuff. And you can order your craft to fire from their maximum combat range, hence making even your lowly Interceptors effectively invulnerable. Battleships are immune to this tactic and do deal massive amounts of damage, but this can be mitigated by attacking them with multiple ships at the same time - the damage gets spread out (dividing repair times amonst the ships present) and the UFO goes down faster (meaning it deals less damage in the first place).
Smoke grenades are remarkably effective at decreasing the aliens' initial advantage; just drop it at the foot of the transport's ramp, before leaving, and the chances of the aliens' reaction fire hitting the redshirts drops drastically. Proximity grenades are sworn by for many players to mine UFO exits and buildings aliens might be hiding in. Both together are a potent combination, especially if you've mined a Zombie that turns into a Chrysalid.
Running low on money in TFTD? Go into business selling Craft Gauss Cannon. Even after having to pay for the workshop space and technicians and the construction cost, you can make a killing doing this.
Not to mention X-Com Apocalypse's Toxigun. An insanely powerful weapon that costs just a pair of A Ps per shot to fire and completely surpasses the aliens' Disruptor Shields. After researching this and the Personal Teleporter, the game pretty much turns into administering point-blank euthanasia shots to the aliens. Even more ridiculously overpowered Alien Gas Grenades and Alien Gas Rockets are available late in the game, provided you manage to capture the Alien Queen live. The Personal Teleporter allows you to instantly teleport your soldiers anywhere on the map, and it is not uncommon to win the mission on the first turn considering that your soldiers are likely people of mass destruction by the time you research this item.
Spiritual SuccessorsUFO: Aftermath and Aftershock had warp weapons. Subverting the previously established player knowledge of armor=longevity, warp weapons inflict greater damage if the target is wearing armor. Devastating when first encountered, when the weapons are reverse-engineered by the player, they become the single most devastating weapon in the game, capable of one-shot killing anything, as enemies are always wearing heavy armor at that point. Greatly toned down in UFO: Afterlight, as the player only gets two warp weapons, with six shots each that can't be recharged during a mission and low base accuracy.
UFO: Aftershock has psionics with level 3 sniper, using the .50 calibre rifle with accuracy add-on and accuracy boosting psi-gear has a 1.1 - 110% chance of a torso hit. A headshot is merely 100% chance of instantly killing the standard mutant or Wargot. Also you can field a whole team of these girls, and depending on the status of your install the accuracy aura buffs may stack. Gets more insane if you give them Katanas against Wargots in room-to-room combat...
Even against enemies that could take multiple headshots and survive, a called shot to the head is considered a critical hit and topples the target over (there are enemies with "knock back resistance" ability but they are not common). Guess how much time it takes to stand up? Approximately same amount as making another called shot. If there is another enemy between sniper and target, then there is chance of hitting the enemy blocking vision, and if this happens, that enemy will be critically hit as if it was intended target of called shot, even if it is impossible to make called shot on that enemy. Very effective against mutants and Starghost combat drones.
UFO Aftershock has also short range game breaker. Guns Akimbo. Well developed Cyborg/Ranger/Commando with 2 MP5 SMGs, armour piercing ammo and proper implants has greater range than assault rifles, 10 shot long burst (each shot has individual check for critical hit meaning that at least one critical hit in burst is virtually certain), very low aiming time (if enemy comes from beyond the corner it is possible to kill him before he finishes turning around) and (due to bug) insane movement speed, team him with Human Scout/Ranger/Commando who has much lower range but (even) higher critical hit chance and can spot living target from half the map. That duo can: shred anything into pieces at short range, suppress and outgun anything at medium range, rush from cover to cover so quickly that no enemy can even aim at them and obviously spot targets for snipers. Only drawback: huge ammo consumption.
XCOM: Enemy Unknown: Snipers. Oh sweet heavens, snipers. A mid-level sniper with the abilities Squad Sight (lets the entire team do spotting for the sniper) and Damn Good Ground (gives additional bonuses for elevation), when given a skeleton suit or a ghost suit, can just camp out on a high building or object, and pick off enemies as the other party members locate them. As long as there is nothing directly between the sniper and the target, it can be shot, and with better accuracy than the character closer to it. On terror missions, two or three snipers with laser weapons at least and a little elevation can one shot chryssalids (and believe me, you definitely want those down quickly) with a headshot.
But wait, there's more: The ability Opportunist removes the aim penalty for overwatch and other reaction shots, and allows reaction fire to score critical hits. This means that if a sniper is on overwatch, and the enemy comes in sight of the sniper (or with Squadsight, any player on the field and there is an open shot between enemy and sniper), it's a much easier and deadlier hit. And then there's In The Zone and Double Tap, the final abilities: In The Zone allows a sniper to take an extra attack if the last shot was made at an uncovered or flanked enemy. Combined with Archangel armor, this can destroy an entire attacking force in one turn, at the risk of your own sniper being out of cover. Double Tap allows a second shot if your sniper doesn't move on his turn. This means your sniper can fire twice if he doesn't move. Once a sniper is in a good position to attack, he no longer needs to move, and on many maps (even the really big ones) it's possible for your sniper to be on one end of the map, and take down with devastating accuracy enemies on the opposite end. Three snipers at Colonel rank with Plasma weapons can fire at least 6 shots a round, with each shot doing enough damage to drop anything less powerful than a Cryssalid with one shot. Enemies typically travel in groups of three, meaning that unless you get attacked by 2 or more groups at once, you can wipe them all out with shots to spare. If your team is half Snipers, half Assaults, your assaults can track down enemies quickly and your Snipers can pick them off as they are found.
Oh, and with In The Zone, this allows you to devastate the most dangerous enemies in the game: Chyssalids, Ethereals, Muton Berserkers, and Sectopoids. All four ignore cover, so with a full clip, it's possible to just unload with sniper shots until they die.
Squadsight Snipers are fearsome orbital cannons of death once armed with Archangel Armor and Plasma Sniper Rifles, yet the alternative, the Snapshot Sniper, is also a mobile engine of death. With a good suit of Ghost or Archangel Armor, a Snapshooter can mow down cover-ignoring enemies with In The Zone giving them lots of free shots, then take to the air with the Archangel or grapple to a vantage point with the Ghost armor, then they start snap-shooting the now-flanked enemies with more ITZ attacks with their Snapshot accuracy penalty negated by the combination of height advantage, the use of the SCOPE item, and flanking.
No longer this in Enemy Within due to the new enemies introduced avert the Complacent Gaming Syndrome. Seekers, speficially are introduced specifically to kill isolated snipers releying on squadsight.
Ghost Armor is the most fearsome suit of armor X-Com has ever produced. Despite its lighter protection than the Titan Armor, it gives a +20 evasion bonus, a passive movement range bonus, plus it comes with a Grappling Hookand 4 charges of invisibility! Being invisible not only prevents Aliens from seeing you, it also gives you a +100 bonus to critical hit rates. Apart from being able to position your squad for perfect ambushes with impunity and no fear of being shot at, your Snipers and Assaults can use the invisibility charges to give them free killer critical hits with their powerful weapons.
Snipers combined with Heavies are flat out unfair against cover-using enemies: Oh, you want to hide behind cover? BOOM!!! Where's your cover now? In pieces on the floor! You can have heavies with rocket launchers devastate anything your opponents are trying to hide behind, opening up a clear shot for your snipers to pick off all of your enemies with In The Zone.
With Enemy Within, we now have the MEC Trooper, the single most overpowered thing in the game. It's Minigun will shred virtually any early game enemy it encounters, the Kinetic Strike Module can One Hit Kill anything short of a Cyberdisk, Sectopod or Mechtoid, the Flamethrower is easily one of the best AOE attacks in the game (and has the bonus benefit of spreading the flames further than the Cone intended, as well as panicking anyone hit by it) despite it's limited Ammo use, and this is before having a special Class ability. And this is just the Mark I, unupgraded model.
Ontop of this, the Training Roulette and Save Scum Second Wave options can easily become this. Save Scum re-seeds the game when you load a saved game, thus allowing you to keep taking your turn until you get the exact result you want. Training Roulette allows for some unholy cross-class combinations - Snipers with Squadsight, HEAT Ammo and Disabling Shot are possible, and may god help your enemies should he be found to be Psychic or given Gene Mods...